## catwigley81 3 years ago Cannot figure out how to set this problem up Find the average rate of change f(x)=x^3+1 intervals given [2,3] book says the answer is 19, how do they get that? no matter what I do Im not getting the correct answer.

1. MrYantho

$f(x2)-f(x1)/x2-x1$ $f(3)-f(2)/3-2$ $((3)^{3}+1)-((2)^{3}+1)/1$ $(27+1)-(8+1)$ $28-9$ $19$

2. ash2326

we want to find the average rate of change find f'(x)= 3x^2 (df/dx gives the change in f(x) at every instant) now take integral between the limits 2 to 3 Average rate of change= $1/(3-2) \int\limits_{2}^{3} 3x^2 dx$ $= 1/1 * [ x^3]$ from 3 to 2 27-8=19

3. ash2326

we know that average of a function f(x) in the interval [ a,b] is given by $1/(b-a) \int\limits_{a}^{b} f(x) dx$

4. catwigley81

Thank you both! Got it!